Structural studies on 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido[1,2-a]pyrimidines by 1H, 13C and 15N NMR spectroscopy

¹H, ¹³C and ¹⁵N NMR studies demonstrated that 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido-[1,2-a] pyrimidlnes exist as an equilibrium mixture of Z-E isomers in the hydrazono–imino tautomeric form having an exocyclic double bond. Proton-catalysed Z-E interconversion is fast. Substituent and solvent effects revealed that the decisive factors controlling the Z:E ratio are internal hydrogen bonding in the Z-isomer, stabilization by solvation and steric interaction.     

On the Chromatic Number of the Visibility Graph of a Set of Points in the Plane

The visibility graph V(P) of a point set P \subseteq R² has vertex set P, such that two points v,w ∈ P are adjacent whenever there is no other point in P on the line segment between v and w. We study the chromatic number of V(P). We characterise the 2- and 3-chromatic visibility graphs. It is an open problem whether the chromatic number of a visibility graph is bounded by its clique number. Our main result is a super-polynomial lower bound on the chromatic number (in terms of the clique number).     

High temperature determination of the rate coefficient for the reaction H2O + CN → HCN + OH

The rate coefficient, k, of the reaction has been determined in the temperature range 2460–2840 K using a shock tube technique. C₂N₂? H₂O? Ar mixtures were heated behind incident shock waves and the CN and OH concentration time histories were monitored simultaneously using broad-band absorption near 388 nm (CN) and narrow-line laser absorption at 306.67 nm (OH). The rate coefficient expression providing the best fit to the data was with uncertainty limits of about ±45% in the temperature range 2460–2840 K. The rate coefficient of the reverse reaction was calculated using detailed balancing, and its extrapolation to lower temperatures was compared with previously published results.